Not sure I’ve ever seen that before. Two consecutive pick sixes
It's probable that it's never happened, and you'd think Google would find it. A little back-of-the-envelope math with a lot of rounding to keep things easy suggests that the odds are against it ever having happened.
Odds of observing a pick six in an NFL game: 11%
To make the math easy, assume 100 plays per game, and that they're all throws (we'll adjust for that later). That leaves the odds of any given throw being a pick six at 0.0011, and the odds of consecutive plays being a pick six as 0.0011 squared, or 0.00000121.
There's a hundred opportunities to kick off the pick six chain (actually 99, but whatever) in this setup, so the odds of observing consecutive pick sixes in a game are .000121.
That's about 1/8000 games. The NFL has been plus or minus 30 teams for the last few decades, playing a sixteen game schedule. That leaves 16*15 = 240 regular season games (it's actually 256 today), and if we add ten or so playoff games to the 240 estimate for regular season games we get 250 games a year. So it would take thirty-two years to expect to observe consecutive pick-sixes in a game, if all plays were pass attempts.
In practice, the league is about 60/40 pass/run, which means that only about 1/3 of all pairs of consecutive plays will both be passes. So now we're talking ninety-six years, and if we start accounting for the history of a league which had fewer teams that passed the ball less often in the past, the odds of having seen consecutive pick-sixes get even longer.